Required Practical 9 • CH03 / CH05

RP9: pH Titration Curves & Ka Determination

Calibrate a digital pH meter, record continuous acid-base titration curves, locate equivalence point vertical inflections, and deduce the acid dissociation constant (Ka) of a weak acid at the half-neutralisation point.

1. Practical Aim & Weak Acid Equilibria

The aim of Required Practical 9 is to plot a continuous titration curve by recording pH during the addition of a strong base (sodium hydroxide, NaOH) to a weak acid (e.g. ethanoic acid, CH3COOH), and determine the experimental acid dissociation constant (Ka):

Weak Acid Equilibrium & Ka Expression HA(aq) ⇔ H+(aq) + A-(aq)

Ka = ( [H+] * [A-] ) / [HA]
pKa = -log10(Ka)   ⇔   Ka = 10^(-pKa)

2. Digital pH Meter Calibration Protocol

A digital pH electrode measures potential difference across a thin glass membrane sensitive to [H+]. Over time, electrode sensitivity drifts, making pre-experimental calibration mandatory:

Multi-Point Buffer Calibration

  1. Rinse the pH probe thoroughly with deionised water from a wash bottle and gently dab dry with a soft tissue (do not rub the delicate glass bulb).
  2. Immerse the probe into a commercial pH 7.00 standard buffer solution. Adjust the calibration dial until the display reads exactly 7.00.
  3. Rinse the probe again with deionised water.
  4. Immerse the probe into a pH 4.00 standard buffer (and subsequently a pH 10.00 buffer for full-scale calibration). Record the reading and construct a calibration graph (pH meter reading vs true buffer pH).

Why Rinsing with Water is Essential

Transferring the probe directly from one buffer solution to another without thorough washing causes cross-contamination of buffers. Residual acidic or basic droplets on the glass bulb alter the local hydrogen ion concentration, generating invalid calibration curves.

3. Step-by-Step Titration Protocol & Fine Increments

  1. Using a volumetric pipette, transfer 25.00 cm3 of 0.100 mol dm^-3 ethanoic acid into a clean 100 cm3 glass beaker.
  2. Fill a burette with 0.100 mol dm^-3 sodium hydroxide solution, ensuring the tip is full and air bubbles are cleared.
  3. Clamp the calibrated pH electrode vertically in the beaker so the glass bulb is completely submerged in acid but positioned safely above the rotating magnetic stirrer bar.
  4. Turn on the magnetic stirrer at a slow, constant speed to ensure rapid, uniform mixing without splashing.
  5. Record the initial pH before any base is added (V = 0.00 cm3).
  6. Add NaOH from the burette in 1.00 cm3 portions. After each addition, wait 5 seconds for the reading to stabilise and record the pH.
  7. Approaching Equivalence (Near ~22 cm3): As the rate of pH change accelerates (>0.3 pH units per addition), switch to fine dropwise additions (0.10 cm3 increments). This captures the steep vertical inflection accurately.
  8. Continue adding 1.00 cm3 portions past equivalence up to ~30 cm3 until the pH plateaus in the high alkaline range (pH ~ 12).

4. The Half-Neutralisation Point (pH = pKa)

The central theoretical feature of a weak acid-strong base titration curve is the half-neutralisation point:

Mathematical Derivation of pH = pKa 1. The equivalence point occurs when exactly stoichiometric moles of base have neutralised all acid molecules (volume = V_equiv).
2. At exactly half the volume required for neutralisation (V_half = V_equiv / 2), exactly 50% of the initial HA has reacted:
    [HA] = [A-]
3. Substituting into the equilibrium constant expression:
    Ka = ( [H+] * [A-] ) / [HA] = [H+] * ( [A-] / [HA] )
4. Since [A-] / [HA] = 1, it follows that:
    Ka = [H+]
5. Taking the negative logarithm of both sides:
    -log10(Ka) = -log10([H+])  →  pKa = pH at half-neutralisation
6. To find Ka: Ka = 10^(-pH).
Weak Acid - Strong Base Titration Curve (RP9) Weak Acid Titration Curve (Ka at Half-Neutralisation) Volume of 0.100 M NaOH Added / cm3 pH 0 4 7 10 13 V_equiv = 25.0 cm3 Equivalence Point (pH = 8.7) V_half = 12.5 cm3 pH = pKa = 4.76 [HA] = [A-] Buffer Midpoint

5. The Buffer Action Plateau

Notice the extended, gently sloping region between 2 cm3 and 20 cm3 on the curve:

  • This is the acidic buffer region. The solution contains significant, comparable concentrations of both unreacted weak acid (HA) and its conjugate base (A- from the formed sodium salt).
  • Small additions of OH- react with HA to form A- and H2O, preventing sharp rises in [OH-] or drops in [H+].
  • Buffer capacity is highest at V_half, where [HA] = [A-].

6. Indicator Selection Criteria

To titrate accurately without a digital pH meter, an acid-base indicator must be chosen whose pH transition range falls entirely within the steep vertical inflection of the curve:

Indicator pH Transition Range Acid Colour → Base Colour Suitable for Weak Acid + Strong Base?
Phenolphthalein pH 8.3 to 10.0 Colourless → Pink YES: Perfectly suited. The vertical jump occurs between pH 7 and 11. Phenolphthalein changes color sharply at equivalence.
Methyl Orange pH 3.1 to 4.4 Red → Yellow NO: Completely unsuitable. Methyl orange changes color in the acidic buffer region (pH 3-4) long before the vertical equivalence jump is reached.

7. Worked Ka Determination Problem

Worked Example: Calculating Ka from a Titration Curve

Problem: In an RP9 experiment, 25.0 cm3 of an unknown weak monobasic carboxylic acid HA is titrated against 0.100 mol dm^-3 NaOH. The titration curve reveals that:

  • The steep vertical equivalence point inflection occurs at V_equiv = 23.40 cm3 with an equivalence pH of 8.85.
  • At exactly half-neutralisation (V = 11.70 cm3), the measured pH is 4.82.

1. Calculate the acid dissociation constant (Ka) of the weak acid.
2. Calculate the initial concentration of the weak acid solution in mol dm^-3.

Step 1: Determine Ka from pH at half-neutralisation

At half-neutralisation, [HA] = [A-], so pH = pKa.
pKa = 4.82
Ka = 10^(-pKa) = 10^(-4.82) = 1.5136 * 10^-5 mol dm^-3
Ka = 1.51 * 10^-5 mol dm^-3 (3 significant figures)

Step 2: Calculate initial concentration of weak acid

Moles of NaOH at equivalence = c * V = 0.100 * (23.40 / 1000) = 2.34 * 10^-3 mol
Stoichiometry HA : NaOH = 1 : 1
Moles of HA in 25.00 cm3 = 2.34 * 10^-3 mol
Initial [HA] = moles / volume = (2.34 * 10^-3) / 0.02500 = 0.0936 mol dm^-3

Final Answer: Ka = 1.51 * 10^-5 mol dm^-3, [HA] = 0.0936 mol dm^-3

8. Practice Exam Questions

Question 1: In the titration of 25.0 cm^3 of a weak acid with 0.100 mol dm^-3 NaOH, the equivalence point occurs at 20.00 cm^3. At what volume of added NaOH does pH equal pKa?

Show Answer & Explanation

Correct Answer: B

The half-neutralisation point occurs at exactly half the equivalence volume (20.00 / 2 = 10.00 cm^3). Here [HA] = [A-], simplifying the Ka expression so that [H+] = Ka, hence pH = pKa.

Question 2: Why is phenolphthalein a suitable indicator for a weak acid - strong base titration, whereas methyl orange is not?

Show Answer & Explanation

Correct Answer: B

The vertical equivalence section for a weak acid-strong base titration lies in the alkaline region (pH 7-11). Phenolphthalein's range (8.3-10.0) matches this perfectly. Methyl orange changes in the acidic buffer zone, giving a false premature endpoint.

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